using only these number (1,3,5,7,9,11,13,15) answer this equation _+_+_=30

Question

you can use any number twice as long as they are the numbers stated above

 

Answer 1

 

Since the sum of three ODD integers is to be EVEN, your problem has no solution, under the stated restrictions.

The SUM OF any two of those odds is even; then adding another (or same) odd, produces odd result, always.

Answer 2

The problem asks that we find 3 numbers from the given set that add up to 30.  Note that all the numbers in the set are odd, while 30 is even.  The sum of any 3 odd numbers is always an odd number, so it is not possible to find 3 numbers from the given set of odd numbers, which when added, give the even number 30.  This problem, as stated, has no solution.

 

Proof that the sum of 3 odd numbers is always odd:

 

Let N, M, and P be 3 odd numbers.  Then

 

N = 2n + 1

M = 2m + 1

P = 2p + 1

 

where n, m, and p are integers.

 

N + M + P = (2n + 1) + (2m + 1) + (2p + 1)

 

N + M + P = 2(n + m + p) + 3

 

N + M + P = 2(n + m + p + 1) + 1

 

Then N + M + P is odd, because it has the form 2q + 1,

where q is an integer, and q = n + m + p + 1

 

However, you do get 15 + 15 = 30 if you use only 2 numbers instead of 3 (using 15 twice), but that is not how the problem is stated.

 

Amanda,

 

This is a strange problem, since it cannot be solved as stated.  Where did this problem come from?